When performing finite element analysis on a space elevator extending radially outwards from one earth radius to geosync radius...
Can I use a point mass approximation for each 1-km element and for the planet?

Sure, but I think you can solve this analytically for a better result and much less computing time. Remember that you have to put the end station higher than the usual 36000 km because of the weight of the cable which increases the centripetal force.

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Originally Posted by AbsentWizard

What factors should be considered when placing the counterweight station?

Mainly mass, strength of the cable and atmospheric drag. You'll probably have to compensate to remain in the right position anyway, so you probably don't need to take relativity into account.
EDIT: on second thought, I wonder whether a counterweight is a good idea. If the main elevator moves up at constant speed, the counterweight initially would have to move down at a much higher speed and gradually slow down. Coriolis forces partially negate this problem, but still.

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Originally Posted by AbsentWizard

How do I rule the unique properties of the artificial gravity of a spinning O'Neill cylinder?

Depends how fast you spin and how close to the centre you are. Otherwise not that different from normal gravity.

I don't think so, but you can have an amulet of mighty fist or have (greater) magic fang permanencied.

I don't know if there are official solutions for special weapon abilities such as flaming or shocking, but you might be able to convince your DM to allow adding them to the amulet. Another option I heard of is enchanted gloves or enchanted claw extensions.

The Reaping Mauler's a trap because its abilities pretty much useless. They're incredibly niche to the point that you'll hardly ever be able to use them. Also, they depend on grappling rules, which suck. And they're slow.

First, all its abilities revolve around grappling. There are too many ways that can be rendered useless. Freedom of Movement alone makes every trick the class has useless. Overly large opponents can't be grappled. A lot of the enemies you can grapple have extreme strength and high fortitude saves, so your chances of successfully grappling 'em are fairly low and a DC... 17, maybe, fortitude save isn't much at all.

The big one, however, is this. It takes a long time to pull off the Reaping Mauler's only trick. You need to pin the enemy. That means taking multiple rounds in which you must win every grapple check, just to force the enemy to make a mediocre save, which they'll probably succeed on, and as your level goes up, the ability becomes less and less effective, since enemies' saves increase. And you can only even face off against one enemy at a time, spending 5+ rounds sitting around with that one enemy, waiting for it to fail its save, in a game where the party is usually very much outnumbered.

In general, Monks hoard pretty much all pugilism while sucking a lot and make it an annoying mess to make a good pugilist. Sacred Fist is a good class. It keeps unarmed damage progression and gets a lot of spellcasting. A Monk1/Cleric6/Sacred Fist10/[Anything that gets you 3 more caster levels]3 still gets level 9 spells, you have your casting stat pouring into AC, you have some stout buffmongering going, et cetera, all without leaving the religious concept of a Monk.

Alternately, if you can get the prerequisites for Ur-Priest on a Monk, then use Ur-Priest casting to qualify for Sacred Fist, two levels of Ur-Priest and ten levels of Sacred Fist will get you ninth level spells by level 20 and still leave eight levels to do with as you please, even if those classes don't have any casting to speak of at all. The skills are a bit of a bitch, though. Between Swashbuckler and Monk, you can cover most of the ridiculous skill requirements except for Spellcraft and Knowledge: The Planes... which is actually a bigger kink than I would hope... Oy, what could get those two without being too random?

That's your prejudice showing, Roy. Granted, the Reaping Mauler is a trap for the unwary, and Swashbuckler or Monk are good only for short dips, but they're decent for that at the beginning.

Swashbucklers have nothing to do with fighting unarmed. It's also a 3 level long class. Reaping Mauler is a grappling class that makes you worse at grappling and actually does nothing for unarmed. Yeah, have fun trying to grapple stuff when you're stuck being Medium or smaller, because you have to have some feat to get in which requires that and only grants a pathetic defense against grappling, doing nothing to help the offense. In other words, Clever Wrestling + 5 levels of Reaping Mauler < Close Quarters Combat and 5 levels of nothing... that is to say, being 5 levels lower. Monk is the only one that actually is unarmed focused. It's still a bad class, but it's the only one on that list pointing in the right direction.